Theorem orel2 213

Description: Elimination of disjunction by denial of a disjunct. Theorem *2.56 of [WhiteheadRussell] p. 107.

Assertion

Ref	Expression
orel2	⊢ (¬ φ → ((ψ ∨ φ) → ψ))

Proof of Theorem orel2

Step	Hyp	Ref	Expression
1		orel1 212	. 2 ⊢ (¬ φ → ((φ ∨ ψ) → ψ))
2		orcom 209	. 2 ⊢ ((ψ ∨ φ) ↔ (φ ∨ ψ))
3	1, 2	syl5ib 181	1 ⊢ (¬ φ → ((ψ ∨ φ) → ψ))

Syntax hints:  ¬ wn 1   → wi 2   ∨ wo 195

This theorem is referenced by:  prel12 1875  funun 2700

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-or 197

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